This talk will be a combination of a meta discussion about how I developed my research program and the main contributions of some of my projects. Specifically, I will share my journey to find a research program that simultaneously engages both equity and cognitive research. I will discuss connections between my work and Funds of Knowledge, as well as other anthropology-informed work, like Ethnomathematics and studies of the mathematics of Indigenous communities. I will share how one of my current projects with Marta Civil, Project AdeLanTe, implements the principles of anti-deficit learning
and teaching, while also building on principles from Funds of Knowledge and Culturally Relevant Pedagogy. In Room 252 Erickson and on Zoom: https://msu.zoom.us/j/98177166186
Password: PRIME

This talk is aimed more at the general audience.
A fundamental question in the representation theory of semisimple Lie groups is to classify their irreducible unitary representations. A guiding principle here is the
Orbit method, first discovered by Kirillov in the 60's for nilpotent Lie groups. It states that the irreducible unitary representations should be related to coadjoint orbits, i.e., the orbits of the Lie group action in the dual of its Lie algebra.
Passing from orbits to representations could be thought of as a quantization problem and it is known that in this setting this is very difficult. For semisimple Lie groups it makes sense to speak about nilpotent orbits, and one could try to study representations that should correspond to these orbits via the yet undefined Orbit method. These representations are called unipotent: they are expected to be nicer than general ones, while one hopes to reduce the study of general representations to that of unipotent ones. I will concentrate on the case of complex Lie groups. I will explain how recent advances in the study of deformation quantizations of singular symplectic varieties allow to define unipotent representations and obtain some results about them. The talk is based on the joint work with Lucas Mason-Brown and Dmytro Matvieievskyi.

In analysis we tend to focus on the "small scale" structure of a space. For example, both derivatives and continuity only depend on a very small neighborhood around a point. Coarse geometry on the other hand focuses on the "large scale" structure of a space. Coarse spaces generalize metric spaces in a way that provides an appropriate framework to study large-scale geometry. Coarse geometry is used to study: higher index theory, elliptical operators, the coarse Baum-Connes conjecture and as a consiquence the Novikov conjecture.
In this talk we will discuss what a coarse structure is, both in terms of metric spaces and in full generality. Then we will look at a few examples. Next, We will introduce uniform Roe algebras and examine their relationship to coarse structures along with recent advances in solving the rigidity problem. Then, time permitting, we will look at uniform Roe modules.

Abstract: Preparation of entangled states via engineered open quantum systems is proven to be successful. In our work, we initiate a study of engineered open quantum systems which drive the states to a subspace. In other word, our system will be non-ergodic. We prove some stability results and large deviation phenomenon in this setting, under some symmetry condition on the Liouvillian. This is joint work with Marius Junge and Nicholas Laracuente.

Given a Legendrian Knot L in a contact 3 manifold, one can associate a so-called LOSS invariant to L which lives in the knot Floer homology group. We prove that the LOSS invariant is natural under the positive contact surgery. In this talk I will review some background and definition, get the idea of the proof and try to focus on the application which is about new examples of non-simple knots.

In their celebrated proof of the Property P Conjecture and its sequel, Kronheimer and Mrowka proved that the fundamental group of r-surgery on a nontrivial knot in the 3-sphere admits an irreducible SU(2)-representation whenever r is at most 2 in absolute value (which implies in particular that surgery on a nontrivial knot is never a homotopy 3-sphere). They asked whether the same is true for other small values of r -- in particular, for r = 3 and 4 -- noting that it's false for r = 5 since 5-surgery on the right-handed trefoil is a lens space. I'll describe recent work which answers their question in the affirmative. Our proof involves Floer homology and also the dynamics of surface homeomorphisms. All of this work is joint with Steven Sivek, and significant parts are also joint with Zhenkun Li and Fan Ye.

Over the last thirty years, there has been various work on simplicial complexes defined from graphs, much from a topological viewpoint. In this talk I will present recent work (with many collaborators) on the topology of two families of simplicial complexes. One is the matching complex, the complex whose faces are sets of edges that form a matching in a graph, with new results on planar graphs coming from certain tilings. The other is the cut complex, where the facets are sets of vertices whose complements induce disconnected graphs.

In this talk, we will share some of our past, present, and future efforts to support students’ defining and conjecturing activity. We will engage in some of the tasks that we are currently implementing with two calculus students. We will also discuss two future directions of our work: optimizing our task design for the whole class setting to promote equitable participation and developing science-based motivational tasks that elicit informal ideas about calculus concepts.

Big data has revolutionized the landscape of computational mathematics and has increased the demand for new numerical linear algebra tools to handle the vast amount of data. One crucial task is to efficiently capture inherent structure in data using dimensionality reduction and feature extraction. Tensor-based approaches have gained significant traction in this setting by leveraging multilinear relationships in high-dimensional data. In this talk, we will describe a matrix-mimetic tensor algebra that offers provably optimal compressed representations of multiway data via a family of tensor singular value decompositions (SVDs). Moreover, using the inherited linear algebra properties of this framework, we will prove that these tensor SVDs outperform the equivalent matrix SVD and two closely related tensor decompositions, the Higher-Order SVD and Tensor-Train SVD, in terms of approximation accuracy. Throughout the talk, we will provide numerical examples to support the theory and demonstrate practical efficacy of constructing optimal tensor representations.
This presentation will serve as an overview of our PNAS paper "Tensor-tensor algebra for optimal representation and compression of multiway data" (https://www.pnas.org/doi/10.1073/pnas.2015851118).

In this talk we consider the entropy theory for singular vector fields with all singularities hyperbolic and non-degenerate. We will construct a countable partition with the property that the metric entropy for any ergodic invariant measure is finite. For singular star flows, we will show that this partition is generating. This is a joint work with Yi Shi and Jiagang Yang.

A fundamental question for any knot invariant asks which knots it detects (if any). For example, it is famously open whether the Jones polynomial detects the unknot. I'll focus in this talk on the detection question for knot invariants coming from Floer theory and the Khovanov--Rozansky link homology theories. I'll survey the progress made on this question over the past twenty years, and will gesture at some of the topological ideas that go into my recent work with Sivek. I'll end with applications of our results to problems in Dehn surgery, explaining in particular how we use them to extend some of Gabai's work from the eighties.

The application of Artificial Intelligence/Machine Learning (AI/ML) in drug development is expanding rapidly. AI/ML have the potential to improve the efficiency of drug development and advance precision medicine. However, there are unique challenges. The presentation will mainly focus on the topic of AI/ML applications in clinical trials, including the following parts:
1. The increasing numbers of submissions over years.
2. Hot therapeutic areas of AI/ML submissions.
3. Types of analysis and objectives in AI/ML in submissions.
4. Case examples.
5. Challenges and outlooks.
In the end of the presentation, opportunities of FDA-ORISE fellowship will be introduced to senior PhD students.

Speaker: Terry Haut, Lawerence Livermore National Lab

Title: An Overview of High-Order Finite Elements for Thermal Radiative Transfer

Date: 03/17/2023

Time: 4:00 PM - 5:00 PM

Place: C304 Wells Hall

Contact: Mark A Iwen ()

In this talk, I will give an overview of numerical methods for thermal radiative transfer (TRT), with an emphasis on the use of high-order finite elements for their solution. The TRT equations constitute a (6+1)-dimensional set of nonlinear PDEs that describe the interaction of a background material and a radiation field, and their solution is critical for modeling Inertial Confinement Fusion and astrophysics applications. Due to their stiff nature, they are typically discretized implicitly in time, and their solution often accounts for up to 90% of the runtime of multi-physics simulations. I will discuss some recently developed linear solvers, physics-informed preconditioners, and methods for preserving positivity that are used to make the solution to the TRT equations efficient and robust.